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Strong unique continuation for a class of degenerate elliptic operators |
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| รหัสดีโอไอ | |
| Creator | Ferit Gurbuz |
| Title | Strong unique continuation for a class of degenerate elliptic operators |
| Contributor | Ahmed Loulit |
| Publisher | Maejo University |
| Publication Year | 2569 |
| Journal Title | Maejo International Journal of Science and Technology |
| Journal Vol. | 20 |
| Journal No. | 2 |
| Page no. | 138 |
| Keyword | unique continuation, Kato class, degenerate elliptic operators, semigroups of operators, partial differential equations |
| Website title | Maejo International Journal of Science and Technology |
| ISSN | 1905-7873 |
| Abstract | The unique continuation property for solutions of second-order elliptic equations has been widely studied owing to its fundamental role in partial differential equations and related fields. While extensive results are available for strictly elliptic operators, comparatively little is known in the degenerate setting. In this paper we establish a strong unique continuation property for a class of degenerate elliptic operators involving potentials in the Kato class. The analysis is carried out under minimal regularity assumptions and the results extend several known contributions in the literature. In particular, we show that solutions that vanish in a neighbourhood, or satisfy appropriate vanishing conditions, must be identically zero. The theoretical findings are further supported by an illustrative example, highlighting the behaviour of solutions and confirming the robustness of the unique continuation property even in the presence of degeneracy and singular potentials. |
